Commerce

Yes, Mathematics is a necessary subject as CAT has one section dedicated to Mathematics. Also half the courses that are being taught in IIMs are maths based. However being a commerce graduate you are not at all in a disadvantaged position. There are a lot of commerce graduates studying in IIMA. They don't actually cover advanced mathematics like calculus.

A degree from a private university (holding ugc/aicte accredition) in regular mode has same value as a degree awarded by government university. But, a regular degree has no comparision with part time/distance mode. Regular is much much more acceptable in industry. All the best

there can be many like bba , b.com ,etc. after that u may pursue MBA

The job opportunities are not very exciting after bcom
You could get junior accountant job with low pay of 10000pm
But you need to know advanced excel and tally so you could learn that
other than that mostly sales jobs are offered
So learning further would be good
professional courses like company secretary if you like companies laws
actuaries if you like insurance sector
For post graduation CFA or MBA
you could do a job and do certificate course like CFP or CCRA
Or you could join internship where you could be accepted as permanent employee

Doesn't matter which line you choose. Just you need to complete your graduation. Arts might be helpful to you.